03 Amplitude Modulation
_____ Notes _____
PCS/PCN
_____ Notes _____
PCS/PCN
_____ Notes _____
Contents
3.0 Amplitude Modulation
3.1 Theory
3.2 AM Receivers
3.2.1 TRF [Tuned Radio Frequency] Amplifier
3.2.2 Superheterodyne Receiver
3.2.3 AM Detection
3.3 AM Modulators
3.3.1 Switching Modulators
3.3.2 Modulation Index Measurement
3.3.3 Quadrature AM Stereo
3.4 DSBSC
3.4.1 Double Balanced Ring Modulator
3.4.2 Push Pull Square Law Balanced Modulator
3.5 SSB
3.5.1 SSB Receivers
3.5.2 Filter Method
3.5.3 Phase Shift Method
3.5.4 Weaver Method
3.0Amplitude Modulation
http://www.educatorscorner.com/experiments/spectral/SpecAn5.html
Information can be used to modulate a high frequency carrier in
three principle ways: by varying the carrier amplitude, frequency
or phase.
The simplest and most bandwidth efficient of these methods is
amplitude modulation.
3.1Theory
A sinewave carrier signal is of the form
and a sinewave modulation signal is of the form
.
Notice that the amplitude of the high frequency carrier takes on
the shape of the lower frequency modulation signal forming what is
called a modulation envelope.
EMBED Word.Picture.8
The modulation index is defined as the ratio of the modulation
signal amplitude to carrier signal amplitude.
where
.
The overall signal can be described by:
A note on frequency multiplication:
The product of two sinewaves produces sum and difference
frequencies:
The subtraction of two frequencies does not result in a negative
frequency. It is understood to really represent the absolute
magnitude:
One way to avoid a negative frequency is to always subtract the
smaller value from the larger one. However, when this expression
refers only to angles, it is often necessary to retain the
negative.
As a result, expanding the instantaneous AM expression results
in:
From this we observe that upper and lower sidebands are created
when using amplitude modulation. The sideband amplitude is:
, and the total occupied spectrum is twice the bandwidth of the
modulation signal or
.
Often, the amplitude of the carrier is normalized and the
expression is written:
AM signals are often characterized in terms of power, since it
is power, which is used to drive antennas. The total power in a 1
resistor is given by:
From this we observe that with a modulation index of 0, the
transmitted power is equal to the carrier power. However, when the
modulation index is 1, the total transmitted power increases to 1.5
times the carrier power.
At 100% modulation, only 1/3 of the total power is in the
sidebands or only 1/2 of the carrier power is in the sidebands.
In terms of voltages and currents:
If the carrier is modulated by a complex signal, the effective
modulation can be determined by the combining the modulation index
of each component.
3.2AM Receivers
RF & IF Digitization in Radio Receivers by Wepman &
Hoffman
The most common receivers in use today are the super heterodyne
type. They consist of:
Antenna
RF amplifier
Local Oscillator and Mixer
IF Section
Detector and Amplifier
SystemView AM Receiver Model
The need for these subsystems can be seen when one considers the
much simpler and inadequate TRF or tuned radio frequency
amplifier.
3.2.1TRF Amplifier
It is possible to design an RF amplifier to accept only a narrow
range of frequencies, such as one radio station on the AM band.
EMBED Word.Picture.8
By adjusting the center frequency of the tuned circuit, all
other input signals can be excluded.
EMBED Word.Picture.8
The AM band ranges from about 500 KHz to 1600 KHz. Each station
requires 10 KHz of this spectrum, although the baseband signal is
only 5 KHz.
Recall that for a tuned circuit:
. The center or resonant frequency in an RLC network is most
often adjusted by varying the capacitor value. However, the Q
remains approximately constant as the center frequency is adjusted.
This suggests that as the bandwidth varies as the circuit is
tuned.
For example, the Q required at the lower end of the AM band to
select only one radio station would be approximately:
As the tuned circuit is adjusted to the higher end of the AM
band, the resulting bandwidth is:
A bandwidth this high could conceivably pass three adjacent
stations, thus making meaningful reception impossible.
To prevent this, the incoming RF signal is heterodyned to a
fixed IF or intermediate frequency and passed through a constant
bandwidth circuit.
3.2.2Superheterodyne Receiver
EMBED Word.Picture.8
The RF amplifier boosts the signal into the mixer. In doing so,
it may add some noise.
1 MHz AM Carrier into the mixer
The other mixer input is a high frequency sinewave. In AM
receivers, it is 455 KHz above the incoming carrier frequency.
An ideal mixer will combine the incoming carrier with the local
oscillator to create sum and difference frequencies.
Integrated LNA & Mixer Basics by National Semiconductor
Operating & Evaluating Quadrature Modulators for PCS Systems
by National Semiconductor
SystemView Mixer Models
Ideal Mixer Output
A real mixer combines two signals and creates a host of new
frequencies:
A dc level
The original two frequencies
The sum and difference of the two input frequencies
Harmonics of the two input frequencies
Sums and differences of all of the harmonics
Non-Ideal Mixer Out
The principle mixer output signals of interest are the sum and
difference frequencies, either of which could be used as an IF.
However, the IF is generally chosen to be lower than the lowest
frequency being received. Consequently, the IF in an AM radio has
been standardized to 455 KHz.
3.2.2.1Local Oscillator Frequency
Since the mixer generates sum and difference frequencies, it is
possible to generate the 455 KHz IF signal if the local oscillator
is either above or below the IF. The inevitable question is which
is preferable.
Case IThe local Oscillator is above the IF. This would require
that the oscillator tune from (500 + 455) KHz to (1600 + 455) KHz
or approximately 1 to 2 MHz.
It is normally the capacitor in a tuned RLC circuit, which is
varied to adjust the center frequency while the inductor is left
fixed. Since
, solving for C we obtain
. When the tuning frequency is a maximum, the tuning capacitor
is a minimum and vice versa. Since we know the range of frequencies
to be created, we can deduce the range of capacitance required.
Making a capacitor with a 4:1 value change is well within the
realm of possibility.
Case IIThe local Oscillator is below the IF. This would require
that the oscillator tune from (500 - 455) KHz to (1600 - 455) KHz
or approximately 45 KHz to 1145 KHz, in which case:
3.2.2.2Image Frequency
Just as there are two oscillator frequencies, which can create
the same IF, two different station frequencies can create the IF.
The undesired station frequency is known as the image
frequency.
EMBED Word.Picture.8
SystemView Image Frequency Model
If any circuit in the radio front end exhibits non-linearities,
there is a possibility that other combinations may create the
intermediate frequency.
3.2.3AM Detection
There are two basic types of AM detection, coherent and
non-coherent. Of these two, the non-coherent is the simpler
method.
Non-coherent detection does not rely on regenerating the carrier
signal. The information or modulation envelope can be removed or
detected by a diode followed by an audio filter.
Coherent detection relies on regenerating the carrier and mixing
it with the AM signal. This creates sum and difference frequencies.
The difference frequency corresponds to the original modulation
signal.
Both of these detection techniques have certain drawbacks.
Consequently, most radio receivers use a combination of both.
3.2.3.1Envelope Detector
EMBED Word.Picture.8
An envelope detector is simply a half wave rectifier followed by
a low pass filter. In the case of commercial AM radio receivers,
the detector is placed after the IF section. The carrier at this
point is 455 KHz while the maximum envelope frequency is only 5
KHz. Since the ripple component is nearly 100 times the frequency
of the highest baseband signal and is not passes through any
subsequent audio amplifiers.
SystemView AM Detector Models
An AM signal where the carrier frequency is only 10 times the
envelope frequency would have considerable ripple:
EMBED Word.Picture.8 3.2.3.2Synchronous Detector
In a synchronous or coherent detector, the incoming AM signal is
mixed with the original carrier frequency.
EMBED Word.Picture.8
SystemView Model
Since the AM input is mathematically defined by:
At the multiplier output, we obtain:
The high frequency component can be filtered off leaving only
the original modulation signal.
This technique has one serious drawback. The problem is how to
create the exact carrier frequency. If the frequency is not exact,
the entire baseband signal will be shifted by the difference. A
shift of only 50 Hz will make the human voice unrecognizable.
Consequently, most radio receivers use an oscillator to create,
not the carrier signal, but another intermediate frequency. This
can then be followed by an envelope detector.
3.2.3.3Squaring Detector
The squaring detector is also a synchronous or coherent
detector. It avoids the problem of having to recreate the carrier
by simply squaring the input signal. It essentially uses the AM
signal itself as a sort of wideband carrier.
EMBED Word.Picture.8
SystemView Model
The output of the multiplier is the square of the input AM
signal:
Since the input is being multiplied by
, one of the resulting terms is the original modulation
signal.
The principle difficulty with this approach is trying to create
a linear, high frequency multiplier.
3.3AM Modulators
A basic equation describing amplitude modulation is:
From this we notice that AM involves a process of
multiplication. There are several ways to perform this function
electronically. The simplest method uses a switch.
3.3.1Switching Modulators
Switching modulators can all be placed into two categories:
unipolar and bipolar.
3.3.1.1Bipolar Switching
The bipolar switch is the easiest to visualize. Note that an AM
waveform appears to consist of a low frequency dc signal whose
polarity is reversing at a carrier rate.
SystemView Bipolar Switching Modulator Model
EMBED Word.Picture.8
The AM signal can be created by multiplying a dc modulation
signal by 1.
EMBED Word.Picture.8
The spectrum of this signal resembles:
If the square wave switching function has a 50% duty cycle, this
simplifies to:
Physically this is done by reversing the signal leads:
EMBED Word.Picture.8
The process of reversing the polarity of a signal is easily
accomplished by placing two switch pairs in the output of a
differential amplifier. The MC1596 is an example of such a
device.
LM1596 Balanced Modulator-Demodulator by National
Semiconductor
EMBED Word.Picture.8
As noted above, a square wave is comprised of an infinite number
of odd harmonics. Consequently multiplying the baseband or
modulation signal by a square wave creates an infinite number of
sum and difference frequencies, each of which constitutes an AM
signal.
EMBED Word.Picture.8
A band pass filter can be used to select any one of the AM
signals. The number of different output frequencies can be
significantly reduced if the multiplier accepts sinewaves at the
carrier input.
Removing the DC component from the input eliminates the carrier
signal and creates DSBSC modulation.
3.3.1.2Unipolar Switching
An AM signal can be created by multiplying a dc modulation
signal by 0 & 1.
EMBED Word.Picture.8 SystemView Unipolar Switching Modulator
The spectrum of this signal is defined by:
Physically this is done by turning the modulation signal on and
off at the carrier rate:
EMBED Word.Picture.8
A high amplitude carrier can be used to turn a diode on and off.
A dc bias is placed on the modulation signal to make certain that
it cannot reverse bias the diode.
EMBED Word.Picture.8
EMBED Word.Picture.8
It may not seem obvious, but the output of this circuit contains
a series of AM signals. A bandpass filter is needed to extract only
one.
3.3.1.3Collector Modulator
The diode switching modulator is incapable of producing high
power signals since it is a passive device. A transistor can be
used to overcome this limitation.
EMBED Word.Picture.8 3.3.1.3Square Law Modulator
The voltage-current relationship of a diode is nonlinear near
the knee and is of the form:
. The coefficients a and b are constants associated with the
diode itself.SystemView Square Law Modulator
EMBED Word.Picture.8
Amplitude modulation occurs if the diode is kept in the square
law region when signals combine.
EMBED Word.Picture.8
Let the injected signals be of the form:
EMBED "Equation" \* mergeformat
The voltage applied across the diode and resistor is given
by:
EMBED "Equation" \* mergeformat
The current in the diode and hence in the resistor is given
by:
From this we observe that passing signals through a nonlinear
device creates a wide range of new signals. Therefore, a band pass
filter is needed to select only the frequencies of interest.
3.3.2Modulation Index Measurement
It is sometimes difficult to determine the modulation index,
particularly for complex signals. However, it is relatively easy to
determine it by observation.
EMBED Word.Picture.8
The trapezoidal oscilloscope display can be used to determine
the modulation index.
EMBED Word.Picture.8
EMBED "Equation" \* mergeformat SystemView Trapezoidal
Pattern
The trapezoidal display makes it possible to quickly recognize
certain types of problems, which would reduce the AM signal
quality.
EMBED Word.Picture.8
The highest authorized carrier power for AM broadcast in the US
is 50 kilowatts, although directional stations are permitted 52.65
kilowatts to compensate for losses in the phasing system. The ERP
can be much higher
3.3.3Quadrature AM Stereo
AM broadcast is inherently monaural, however there are ways to
make it stereophonic.
http://www.inetarena.com/~alfredot/exciter-theory.html
http://www.fcc.gov/mmb/asd/bickel/amstereo.html
At one time, there were five competing systems: Harris,
Magnavox, Motorola, Belar, and Kahn and Hazeltine.
In 1993 the FCC picked C-Quam system. Of the stations then
broadcasting in AM stereo, 591 used Motorola C-Quam, 37 used the
Harris system, and less than 20 used the Kahn system.
There were already 24 million C-Quam receivers.
3.3.3.1AM stereo and Vector Modulation
A simple AM stereo system can be mad using a vector modulator,
unfortunately, it is not backward compatible with monophonic AM
receivers. However, its operating principles form the basis of
those systems in use.
EMBED Word.Picture.8
Output of the top mixer:
EMBED "Equation" \* mergeformat
Output of the bottom mixer:
EMBED "Equation" \* mergeformat
Although the sum of these two signals can easily be detected,
the uncorrelated phase changes between the two sidebands cause
amplitude variations, which cause distortion in a standard envelope
detector.
SystemView Theoretical AM Stereo
3.3.3.2C-QUAM
AM C-QUAM by Harris
X
X
LO
90
o
S
sin
w
c
t
cos
w
c
t
L+R
L
-
R
Limiter
Amplitude
Modulator
The basic idea behind the C-Quam modulator is actually quite
simple. The output stage is an ordinary AM modulator however; the
carrier signal has been replaced by an amplitude limited vector
modulator. Therefore, the limiter output is really a
phase-modulated signal.
A standard AM receiver will detect the amplitude variations as
L+R. A stereo receiver will also detect the phase variations and to
extract LR. It will then process these signals to separate the left
and right channels.
To enable the stereo decoder, a 25 Hz pilot tone is added to the
LR channel.
3.4DSBSC
Double side band suppressed carrier modulation is simply AM
without the broadcast carrier. Recall that the AM signal is defined
by:
EMBED "Equation" \* mergeformat
The carrier term in the spectrum can be eliminated by removing
the dc offset from the modulating signal:
EMBED "Equation" \* mergeformat
One of the circuits which is capable of doing this is the double
balance ring modulator.
3.4.1Double Balanced Ring Modulator
EMBED Word.Picture.8 SystemView Double Balanced Ring
Modulator
If the carrier is large enough to cause the diodes to switch
states, then the circuit acts like a diode switching modulator:
EMBED Word.Picture.8
The modulation signal is inverted at the carrier rate. This is
essentially multiplication by 1. Since the transformers cannot pass
dc, there is no term which when multiplied can create an output
carrier. Since the diodes will switch equally well on either cycle,
the modulation signal is effectively being multiplied by a 50% duty
cycle square wave creating numerous DSBSC signals, each centered at
an odd multiple of the carrier frequency. Bandpass filters are used
to extract the frequency of interest.
Some IC balanced modulators use this technique, but use
transistors instead of diodes to perform the switching.
3.4.2Push Pull Square Law Balanced Modulator
EMBED Word.Picture.8
This circuit uses the same principles as the diode square law
modulator. Since dc cannot pass through the transformer, it would
be expected that there would be no output signal at the carrier
frequency.
The drain current vs. gate-source voltage is of the form:
EMBED "Equation" \* mergeformat
The net drain current in the output transformer is given by:
EMBED "Equation" \* mergeformat
By applying KVL around the gate loops we obtain:
EMBED "Equation" \* mergeformat
Putting it all together we obtain:
EMBED "Equation" \* mergeformat
From this we note that the first term is the originating
modulation signal and can easily be filtered off by a high pass
filter. The second term is of the form:
EMBED "Equation" \* mergeformat 3.5SSB
Single sideband is a form of AM with the carrier and one
sideband removed. In normal AM broadcast, the transmitter is rated
in terms of the carrier power.
SSB transmitters attempt to eliminate the carrier and one of the
sidebands. Therefore, transmitters are rated in PEP [peak envelope
power].
EMBED "Equation" \* mergeformat
With normal voice signals, an SSB transmitter outputs 1/4 to 1/3
PEP.
Modulation
Comments
SSB
Single sideband - amateur radio
SSSC
Single sideband suppressed carrier - a small pilot carrier is
transmitted
ISB
Independent sideband - two separate sidebands with a suppressed
carrier. Used in radio telephone
VSB
Vestigial sideband - a partial second sideband. Used in TV
broadcasting
ACSSB
Amplitude companded SSB
There are several advantages of using SSB:
More efficient spectrum utilization
Less subject to selective fading
More power can be placed in the intelligence signal
10 to 12 dB noise reduction due to bandwidth limiting
3.5.1Filter Method
The simplest way to create SSB is to generate DSBSC and then use
a bandpass filter to extract one of the sidebands.
EMBED Word.Picture.8 SystemView SSB Filter Method
This technique can be used at relatively low carrier
frequencies. At high frequencies, the Q of the filter becomes
unacceptably high. The required Q necessary to filter off one of
the sidebands can be approximated by:
EMBED "Equation" \* mergeformat
Several types of filters are used to suppress unwanted
sidebands:
Filter Type
Maximum Q
LC
200
Ceramic
2000
Mechanical
10,000
Crystal
50,000
Standard Crystal Filters
In order to reduce the demands placed upon the filter, a double
heterodyne technique can be used.
SystemView SSB Filter Method with Double Mixer
EMBED Word.Picture.8
The first local oscillator has a relatively low frequency thus
enabling the removal of one of the sidebands produced by the first
mixer. The signal is then heterodyned a second time, creating
another pair of sidebands. However, this time they are separated by
a sufficiently large gap that one can be removed by the band
limited power amplifier or antenna matching network.
Example
Observe the spectral distribution under the following
conditions:
Audio baseband = 100 HZ to 5 KHz
LO1 = 100 KHz
LO2 = 50 MHz
The spectral output of the first mixer is:
EMBED Word.Picture.8
If the desired sideband suppression is 80 dB, the Q required to
filter off one of the sidebands is approximately:
EMBED "Equation" \* mergeformat
It is evident that a crystal filter would be needed to remove
the unwanted sideband.
After the filter, only one sideband is left. In this example,
well retain the USB. The spectrum after the second mixer is:
EMBED Word.Picture.8
The Q required to suppress one of the side bands by 80 dB is
approximately:
EMBED "Equation" \* mergeformat
Thus, we note that the required Q drops in half.
This SSB filter technique is used in radiotelephone
applications.
3.5.2Phase Shift Method
EMBED Word.Picture.8
The output from the top mixer is given by:
EMBED "Equation" \* mergeformat
The output from the bottom mixer is given by:
EMBED "Equation" \* mergeformat
The summer output is:
. This corresponds to the upper sideband only.SystemView SSB
Phase Shift Model
The major difficulty with this technique is the need to provide
a constant 90o phase shift over the entire input audio band. To
overcome this obstacle, the Weaver or third method uses an audio
sub carrier, which is phase shifted.
3.5.3Weaver Method
The Weaver or third method places the baseband signal on a low
frequency quadrature carrier.
SystemView Model Weaver Method
X
X
LO
1
Audio
Input
90
o
S
X
X
LO
2
90
o
Audio
Subcarrier
LPF
LPF
This has the advantage of not requiring a broadband phase
shifter however; the use of four mixers makes it awkward and seldom
used.
AM Modulation Waveforms
EMBED Word.Picture.8 3.5.4SSB Receivers
These receivers require extremely stable oscillators, good
adjacent channel selectivity, and typically use a double conversion
technique. Envelope detectors cannot be used since the envelope
varies at twice the frequency of the AM envelope.
Stable oscillators are needed since the detected signal is
proportional to the difference between the untransmitted carrier
and the instantaneous side band. A small shift of 50 Hz makes the
received signal unusable.
SSB receivers typically use fixed frequency tuning rather than
continuous tuning as found on most radios. The receiver uses
crystal oscillators to select the fixed frequency channels.
Assignment QuestionsQuick Quiz
1.Double heterodyning cannot be used in SSB transmitters based
on the filter technique. [True, False]
Analytical Questions
1.Determine the carrier power in an AM signal if the total power
is 100 kW and the modulation index is 0.89.
2.Since the voltage-current relationship of a diode is of the
form:
EMBED "Equation" \* mergeformat
it can be used to make an AM modulator or demodulator.
a)State the necessary conditions for this to happen.
b)Create a SystemView model to demonstrate this phenomenon.
c)What impact does this phenomenon have on circuit design?
3.An AM transmitter has the following characteristics:
Carrier frequency = 27 MHz
Carrier power = 10 W
Modulation frequency = 2 KHz sine wave
Modulation index = 90%
Load impedance = 50
Determine:
a)Component frequencies in the AM signal
b)Minimum and maximum voltage of the AM waveform
c)Sideband signal voltage and power
d)Load current
e)Sketch the time domain, frequency domain, and trapezoidal
waveforms
Composition Questions
1.Prove mathematically that under the right set of
circumstances, a switching diode can be used to create AM.
2.Create a SystemView model to show that the following receiver
can detect pure AM stereo.
X
X
LO
90
o
sin
w
c
t
cos
w
c
t
LPF
LPF
Input
Channel
1
Channel
2
3.List the components of an AM signal at 1 MHz when modulated by
a 1 KHz sinewave. What are the component(s) if it is converted to
an USB transmission? If the carrier is redundant, explain why must
it be reinserted at the receiver.
4.Draw the block diagram of a superheterodyne AM receiver.
Assume it is tuned to receive a station centered at 1200 KHz, and
explain in detail what happens at each stage. Use sketches to
supplement your explanations.
5.Given the following SSB transmitter:
EMBED Word.Picture.8
with the following characteristics:
1.Audio input = 100 Hz to 5 KHz
2.LO1 = 100 KHz
3.LO2 = 50 MHz
4. Sideband suppression = 40 dB
5. The filter and power amp only pass the upper sidebands out if
their respective mixers.
Find:
a)The required Q in the filter
b)Sketch and label the expected spectrum at every point in the
circuit
c)Create a SystemView model to verify your answer [Note: it will
be necessary to scale the 50 MHz oscillator frequency]
6.Given the following device:
EMBED Word.Picture.8
a)Identify the circuit
b)Explain its operation using mathematics
c)Illustrate its operation using time and frequency domain
sketches
d)Suggest applications
For Further Research
Amateur Radio
http://www.purchon.co.uk/radio/
http://www.alltel.net/~kj5ag/
http://www.qsl.net/w5ami/
http://www.thebizlink.com/am/
Vintage
http://www.antique-radio.org/
http://www.liveline.com/~w7gmk/vlinks.html
National Association of Broadcasters
http://www.nab.org/
http://www.gate.net/~dlung/rf.html
Radio Theory
http://murray.newcastle.edu.au/users/staff/eemf/ELEC351/SProjects/Bastian/index.htm
CBC Radio
http://radioworks.cbc.ca/
Slide Tutorial
http://www.telecommunication.msu.edu/classes/tc201/slides/Modulation/index.htm
Modulation Tutorial
http://www.ece.utexas.edu/~bevans/courses/realtime/lectures/13_Modulation/lecture13/lecture13.html
Broadcast Equipment
http://www.bdcast.com/home.html
http://www.rfspec.com/
Harris
http://www.comsyst.com.au/harris1.htm
HP AM/FM Tutorial
http://www.tmo.hp.com/tmo/Notes/interactive/an-150-1/download/hp-am-fm.zip
Wireless Communications Systems3
4 - Wireless Communications Systems
Wireless Communications Systems4 -
_941444156.unknown
_1002362709.doc
X
X
LO
1
Audio
Input
90
o
X
X
LO
2
90
o
Audio
Subcarrier
LPF
LPF
_1020261433.doc
X
X
LO
90
o
sin
c
t
cos
c
t
Amplitude
Modulator
Limiter
L-R
L+R
_1002362081.unknown
_1000739027.doc
X
X
LO
90
o
sin
c
t
cos
c
t
LPF
LPF
Input
Channel 1
Channel 2
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